CRYSTALLOGRAPHY. 
such as to shew the decrease of the lamina; 
by rows of particles of such a size as to give 
a surface uneven, similar to a succession of 
steps, it is obvious, that if we substitute for 
this the delicate structure of nature, the 
number of laminse may be so great, and the 
number of their cubical particles such, that 
the depression or channel at their edges 
will be altogether imperceptible to our 
senses, and the surfaces will appear perfect 
planes. 
Such is an example of the production of 
a secondary from a primitive form by a su- 
perposition of laminae, decreasing accoi'd- 
ing to a certain law. It is obvious that the 
laws of decrement may be various, and ac- 
cordingly the decrements stated by Hauy 
are of four different kinds : first, decrements 
on the edges, or parallel to the sides, of the 
primitive form, of which the above is an 
example. 2. Decrements on the angles, 
that is, decrements of which the lines are 
parallel to the diagonals of the faces of the 
primitive form. 3. Intermediate decre- 
ments, or those which are parallel to lines 
situated between the diagonals and edges 
of that form. 4. Mixed decrements, in 
wliich the number of ranges abstracted in 
breadth or in height give proportions, the 
two terms of which are beyond unity. 
These four laws of decrement explain, 
by the modifications of which they are sus- 
ceptible, of all the varieties of form under 
which crystals are presented to us. These 
modifications are reduced to the following : 
1. Sometimes the decrements take place on 
all the edges, or on all the angles. 2. Some- 
times on certain edges or certain angles 
only. 3. Sometimes they are uniform by 
one, two, three ranges, or more. i. Some- 
times the law varies from one edge to ano- 
ther, or from one angle to another. 5. In 
some cases the decrements on the edges 
correspond with the decrements on the 
angles. 6. Sometimes the same edge or 
the same angle undergoes successively se- 
veral laws of decrements. And, lastly, 
there are cases in which the secondary crystal 
has faces parallel to those of the primitive 
form, and which give rise to new modifica- 
tions from their combinations with the faces 
resulting from the decrements. 
With such diversity of laws the number 
of forms which may exist is immense, and 
far exceeds what have been observed. Con- 
fining the calculation to tw o of the simplest 
laws, those which produce subtractions by 
one or two ranges, it is shewn that carbo- 
nate of lime is susceptible of 2044 different 
forms, a number 50 times greater than that 
of the forms already known ; and if decre- 
ments of three and four ranges be admitted 
into the combination, the calculation will 
give 8,388,604 possible forms of the same 
substance. And even this number may be 
much augmented in consequence either of 
intermediate or mixed decrements being 
taken into account. 
In concluding this sketch of Crystallo- 
graphy, which we have extracted from the 
excellent “ System of Chemistry” by Mur- 
ray, we have also thought it proper, with 
him, to give the figures of the more usual 
forms of crystals, and their modifications, 
with the terms and definitions of Werner, 
instead of following Hauy in his minute, 
though valuable details. 
It is necessary to premise, that the parts 
of which a crystal is conceived to be com- 
posed, are planes, edges, and angles. 
Planes, according to the usual geometrical 
definition, are surfaces lying evenly be- 
tween their bounding lines : they are dis- 
tinguished into lateral, which are consider- 
ed as those parts of the surface of the body 
W'hich are of the greatest extent, and which 
form its confines towards its smallest ex- 
tent; and extreme or terminal, which are 
those of smallest extent, and fornr the 
bounds of the body towards its largest ex- 
tent. Edges are formed by the junction of 
two planes under determinate angles ; they 
also are lateral, or those formed by the 
junction of two lateral planes ; and termi- 
nal formed by the junction of two termi- 
nal planes, or of a terminal with a lateral 
plane. Lastly, angles are formed by the 
junction of three or more planes in one 
point. 
Werner admits even primary figures of cry- 
stals which are susceptible of numerous mo- 
difications. These figures are the icosaedron, 
the dodecaedron, the hexaedron, which in- 
cludes the cube and the rhomb, the prism, 
the pyramid, the table, and the lens. 
1st. The icosaedron, fig. 13, is a solid, 
consisting of twenty equilateral triangular 
planes, united under equal angles. 2d. 
The dodecaedron, fig. 14, or solid of 
twelve equal or pentagonal faces. 3d. 
The cube, fig. 15, or solid, composed of 
six quidrilateral planr-s united at right an- 
gles. 4th. The rliomh, fig. 16, or solid, of 
six quadrilateral planes united at oblique 
angles. 5th. The prism, oi- solid, of two ter- 
minal planes, parallel, equal, and siinilm', 
connected by quadrangular lateral planes 
havuig one direction ; the number of late- 
